1. Field of the Invention
This invention relates to a bone measurement method and apparatus. This invention particularly relates to a method and apparatus for acquiring a quantitative index value, which represents a condition of a structure of a bone tissue of a human body, or the like, the condition being useful in making a diagnosis of osteoporosis, or the like, in accordance with a radiation image.
2. Description of the Prior Art
Bone mineral analysis, i.e., quantitative determination of amounts of calcium in bones, is useful for making a diagnosis for preventing fractures of bones.
Specifically, the amounts of the bone mineral are determined by the density of bone trabeculae, which are the cancellous matter constituting the internal regions of bones, i.e. the bone density. Therefore, if the bone density is low, the image density of a bone pattern in a bone image will become high. If the bone density is high, the image density of the bone pattern in the bone image will become low.
Therefore, by investigating small changes in the amounts of calcium contained in bones, osteoporosis can be found early, and fractures of the bones can be prevented.
Various techniques for bone mineral analysis have been proposed and used in practice. Such techniques include microdensitometry (MD technique), single photon absorptiometry (SPA technique), dual photon absorptiometry (DPA technique), quantitative digited radiography (QDR technique), quantitative computer tomography (DQCT technique), and dual energy quantitative computer tomography (DQCT technique).
The above-enumerated techniques are the ones for measuring the so-called xe2x80x9cbone density.xe2x80x9d The bone density has heretofore been utilized popularly as an index value for a diagnosis of osteoporosis. Recently, besides the bone density value, it has been proposed to quantitatively represent the condition of a bone structure as an index value.
Specifically, in a simple sense, the bone density value is the value of the ratio of the mass to the volume. Therefore, the bone density value does not reflect a difference in condition of distribution of bone trabeculae, which are the substance as the bone for supporting a load, i.e. a difference in bone structure. However, primarily, osteoporosis is the problem of the bone strength. The bone strength markedly depends upon the condition of a distribution of bone trabeculae. Therefore, a technique for representing the condition of a bone structure as an index value is a technique useful for a diagnosis of osteoporosis.
By way of example, as an index value for representing the condition of a bone structure, there have heretofore been known a star volume and an index value obtained with node-strut analysis.
As an aid in simplifying the explanation, a processing technique for calculating the star volume as an index value will hereinbelow be referred to as the star volume technique. Also, a processing technique for calculating an index value with node-strut analysis will hereinbelow be referred to as the node-strut analysis technique.
FIG. 3 is an explanatory view showing index values with the star volume technique. In the star volume technique, marrow space star volume (Vm) and trabecular star volume (Vt) are defined. The marrow space star volume (Vm) represents the mean value of the values of the bone marrow cavity volume of the regions, each of which extends from a predetermined point, a, in the bone marrow cavity along every direction without being obstructed by the bone trabeculae. The trabecular star volume (Vt) represents the mean value of the values of the volume of the regions, each of which extends from a point, b, in the bone trabecula along every direction to the end of the bone trabecula. In FIG. 3, the hatched regions indicate the bone trabeculae, and the other region indicates the bone marrow cavity. The star volume is considered as being a gap-free stereological index, which represents the size of the bone trabecula in the bone marrow cavity as a three-dimensional value in units of mm3 or xcexcm3 by elaborating the sampling technique. In cases where the continuity of the bone trabeculae is high, Vm takes a small value. In cases where the level of disappearance or porosity of the bone trabeculae is high, Vm takes a large value. Conversely, in cases where the continuity of the bone trabeculae is high, Vt takes a large value. In cases where the level of disappearance or porosity of the bone trabeculae is high, vt takes a small value.
The value of Vmi at an arbitrary point i in the bone marrow cavity is defined by Formula (1) shown below.
Vmi=(xcfx80/3)xc3x97l0m3xe2x80x83xe2x80x83(1)
In Formula (1), in cases where the length, over which the bone-marrow cavity is continuous along an arbitrary direction extending from the point i, is represented by l0, l0m3 represents the mean value of the values l03 calculated with respect to all of radial directions extending from the point i.
The value of Vtj at an arbitrary point j in the bone trabecula is defined by Formula (2) shown below.
xe2x80x83Vtj=(xcfx80/3)xc3x97xcexa3l14/xcexa3l1xe2x80x83xe2x80x83(2)
wherein l1 represents the length, over which the bone trabecula is continuous along an arbitrary direction extending from the point j. The values of l1 are calculated with respect to all of radial directions extending from the point j, and xcexa3 represents the calculation of the sum of the values with respect to all of the radial directions.
In such cases, Vmi may be calculated for each sampling point, and the mean value of the Vmi values, which have been calculated for all of the sampling points, may be taken as Vm. Also, Vtj may be calculated for each sampling point, and the mean value of the vtj values, which have been calculated for all of the sampling points, may be taken as Vt.
As the index value representing the bone trabecula structure, either one of Vm and Vt may be employed.
Also, for example, as illustrated in FIG. 4, the three-dimensional coordinate system, which has the coordinate axes for the age of an object, the bone density value, and the value of Vt, is formed. A judgment as to the condition of the bone tissue is made in accordance with a position on the three-dimensional coordinate system, at which the received results are plotted. Specifically, in cases where the age of the object, the bone density value, and the value of Vt are located at a point P1, it is judged that the bone tissue is in the condition A (e.g., the condition suspected to be osteoporosis). In cases where the age of the object, the bone density value, and the value of Vt are located at a point P2, it is judged that the bone tissue is in the condition B (the condition requiring care). Also, in cases where the age of the object, the bone density value, and the value of Vt are located at a point P3, it is judged that the bone tissue is in the condition C (the normal condition).
The node-strut analysis technique is a technique for two-dimensionally rating the continuity of the bone trabeculae. Specifically, a connection point, at which three or more bone trabeculae are connected with one another, is defined as a node (Nd) (indicated by the white dot in FIG. 5), and a terminal point, at which the bone trabecula is not connected with other bone trabeculae, is defined as a terminus (Tm) (indicated by the black dot in FIG. 5). As illustrated in FIG. 5, the center lines (struts) of the bone trabeculae, which lines connect the points, are classified into NdNd (the strut connecting the connection points with each other), NdTm (the strut connecting a connection point and a terminal point with each other), TmTm (the strut connecting the terminal points with each other), CtNd (the strut connecting Ct, i.e. the cortical bone, and a connection point each other), and CtTm (the strut connecting the cortical bone and a terminal point with each other). The lengths of the respective struts are measured.
Thereafter, the index values described below are defined in accordance with the lengths of the struts, the number NNd of the connection points Nd, and the number NTm of the terminal points Tm.
(1) Index Value Concerning the Length
The ratio (%) of the length of each strut to the sum TSL of lengths of all struts:
NdNd/TSL 
NdTm/TSL 
TmTm/TSL 
CtNd/TSL 
CtTm/TSL 
(2) Index Value Concerning Length With Respect to Area
The ratio (mm/mm2) of the length of each strut to the area TV of the bone tissue (the sum of the bone trabeculae and the cortical bone, or only the bone trabeculae)
TSL/TV
NdNd/TV
NdTm/TV
TmTm/TV
CtNd/TV
CtTm/TV
(3) Index Value Concerning Number
NNd/TV: Number (/mm2) of the connection points per area of the bone tissue
NTm/TV: Number (/mm2) of the terminal points per area of the bone tissue
NNd/NTm: Ratio of the number of the connection points to the number of the terminal points
With the index values described above, a large value of the index value related to the connection point Nd indicates a high continuity of the bone trabeculae. Also, a large value of the index value related to the terminal point Tm indicates a low continuity of the bone trabeculae.
The node-strut analysis technique is useful as a technique capable of directly and easily measuring the continuity of the bone trabeculae.
However, the aforesaid techniques for acquiring the index values, which represent the condition of the bone structure, have the problems in that a sample of the actual substance, i.e. a sliced specimen of the bone, must be utilized, and therefore the index values cannot be acquired non-invasively from the object body.
Attempt have heretofore been made in order to obtain an index value, which represents the condition of a structure of a bone tissue, in accordance with a radiation image, in which a pattern of the bone tissue is embedded. However, such techniques have the problems in that a practically acceptable measurement accuracy cannot be obtained due to overlapping of the bone tissue pattern upon a soft tissue pattern, fluctuations in image density and contrast, and the like.
The primary object of the present invention is to provide a bone measurement method, with which an index value accurately representing a condition of a structure of a bone tissue is capable of being acquired in accordance with a radiation image.
Another object of the present invention is to provide an apparatus for carrying out the bone measurement method.
A bone measurement method in accordance with the present invention is characterized by carrying out bone tissue pattern emphasis processing in accordance with a morphology operation on an image signal, which represents a radiation image, thereby extracting or emphasizing the pattern of a structure of the bone tissue, and calculating an index value, which represents a condition of the structure of the bone tissue, in accordance with an image, which represents the extracted or emphasized pattern of the structure of the bone tissue.
specifically, the present invention provides a bone measurement method, in which an index value representing a condition of a structure of a bone tissue is acquired, the method comprising the steps of:
i) carrying out bone tissue pattern emphasis processing on a radiation image of an object, which contains at least the bone tissue, the bone tissue pattern emphasis processing being carried out in accordance with a morphology operation, and
ii) carrying out index value acquisition processing on a bone tissue image, which has been obtained from the bone tissue pattern emphasis processing and represents an emphasized pattern of the structure of the bone tissue.
The term xe2x80x9cbone tissuexe2x80x9d as used herein means the bone trabeculae, the bone marrow cavity, which is the cavity other than the bone trabeculae, the cortical bone, which covers the outer peripheries of the bone trabeculae and the bone marrow cavity, and the like. The term xe2x80x9ccondition of a structure of a bone tissuexe2x80x9d as used herein primarily means the condition of distribution of the bone trabeculae and the bone marrow cavity.
As the index value representing the condition of the structure of the bone tissue, it is possible to employ Vm or Vt in accordance with the aforesaid star volume technique. It is also possible to employ NdNd/TSL, NdTm/TSL, TmTm/TSL, CtNd/TSL, CtTm/TSL, TSL/TV, NdNd/TV, NdTm/TV, TmTm/TV, CtNd/TV, CtTm/TV, NNd/TV, NTm/TV, or NNd/NTm in accordance with the node-strut analysis technique, or the like.
As the bone tissue pattern emphasis processing in accordance with the morphology operation, skeleton processing may be employed. The morphology operation will be described hereinbelow.
The morphology operation (hereinbelow also referred to as the morphology processing) is the processing based upon algorithms of morphology, with which only a specific image portion, such as an abnormal pattern, is selectively extracted from an original image. The morphology processing has been studied as a technique efficient for detecting, particularly, a small calcified pattern, which is one of characteristic forms of mammary cancers. However, the image to be processed with the morphology processing is not limited to the small calcified pattern in a mammogram.
The morphology processing is carried out by using a structure element B corresponding to the size and the shape of the image portion to be extracted. The morphology processing has the features in that, for example, it is not affected by complicated background information, and the extracted image pattern does not become distorted.
Specifically, the morphology processing is advantageous over ordinary differentiation processing in that it can more accurately detect the geometrical information concerning the size, the shape, and the image density distribution of the calcified pattern.
How the morphology processing is carried out will be described hereinbelow by taking the detection of a small calcified pattern in a mammogram as an example. (Fundamental operation of morphology processing)
In general, the morphology processing is expanded as the theory of sets in an N-dimensional space. As an aid in facilitating the intuitive understanding, the morphology processing will be described hereinbelow with reference to a two-dimensional gray level image.
The gray level image is considered as a space, in which a point having coordinates (x, y) has a height corresponding to an image density value f(x, y). In this case, it is assumed that the image signal representing the image density value f(x, y) is a high luminance-high signal level type of image signal, in which a low image density (i.e., a high luminance when the image is displayed on a CRT display device) is represented by a high image signal level.
Firstly, as an aid in facilitating the explanation, a one-dimensional function f(x) corresponding to the cross-section of the two-dimensional gray level image is considered. It is assumed that a structure element g used in the morphology operation is a symmetric function of Formula (3) shown below, which is symmetric with respect to the origin.
g3(x)=g(xe2x88x92x)xe2x80x83xe2x80x83(3)
It is also assumed that the value is 0 in a domain of definition G, which is represented by Formula (4) shown below.
G={xe2x88x92m, xe2x88x92m+1, . . . , xe2x88x921, 0, 1, . . . , mxe2x88x921, m}xe2x80x83xe2x80x83(4)
In such cases, the fundamental forms of the morphology operation are very simple operations carried out with Formulas (5), (6), (7), and (8) shown below.
dilation; [f⊕Gs](i)=max{f(ixe2x88x92m), . . . , f(i), . . . , f(i+m)}xe2x80x83xe2x80x83(5)
erosion; [fxe2x8ax96Gs](i)=min{f(ixe2x88x92m), . . . , f(i), . . . , f(i+m)}(6)
opening; fg=(fxe2x8ax96gs)⊕gxe2x80x83xe2x80x83(7)
closing; fg=(f⊕gs)xe2x8ax96gxe2x80x83xe2x80x83(8)
Specifically, as illustrated in FIG. 6A, the dilation processing is the processing for retrieving the maximum value in the region of a width of xc2x1m (which width is the value determined in accordance with the structure element B and corresponds to the mask size shown in FIG. 6A) having its center at a picture element of interest. As illustrated in FIG. 6B, the erosion processing is the processing for retrieving the minimum value in the region of the width of xc2x1m having its center at the picture element of interest. The opening processing is equivalent to the processing in which the dilation processing is carried out after the erosion processing, i.e., the processing in which the maximum value is searched after the searching of the minimum value. Also, the closing processing is equivalent to the processing in which the erosion processing is carried out after the dilation processing, i.e., the processing in which the minimum value is searched after the searching of the maximum value.
More specifically, as illustrated in FIG. 6C, the opening processing is equivalent to the processing for smoothing the image density curve f(x) from the low luminance side, and removing a convex image density fluctuating portion (i.e., the portion at which the luminance is higher than that of the surrounding portions), which fluctuates in a region spatially narrower than the mask size of 2m.
Also, as illustrated in FIG. 6D, the closing processing is equivalent to the processing for smoothing the image density curve f(x) from the high luminance side, and removing a concave image density fluctuating portion (i.e., the portion at which the luminance is lower than that of the surrounding portions), which fluctuates in the region spatially narrower than the mask size of 2m.
In cases where the structure element g is not symmetric with respect to the origin, the dilation operation with Formula (5) is referred to as the Minkowski sum, and the erosion operation with Formula (6) is referred to as the Minkowski difference.
In cases where the image signal representing the image density value f(x) is a high image density-high signal level type of image signal, in which a high image density is represented by a high image signal level, the relationship between the image density value f(x) and the image signal value becomes reverse to the relationship between the image density value f(x) and the image signal value in the high luminance-high image signal level type of image signal. Therefore, the dilation processing, which is carried out on the high image density-high signal level type of image signal, coincides with the erosion processing, which is carried out on the high luminance-high signal level type of image signal as shown in FIG. 6B. The erosion processing, which is carried out on the high image density-high signal level type of image signal, coincides with the dilation processing, which is carried out on the high luminance-high signal level type of image signal as shown in FIG. 6A. The opening processing, which is carried out on the high image density-high signal level type of image signal, coincides with the closing processing, which is carried out on the high luminance-high signal level type of image signal as shown in FIG. 6D. Also, the closing processing, which is carried out on the high image density-high signal level type of image signal, coincides with the opening processing, which is carried out on the high luminance-high signal level type of image signal as shown in FIG. 6C.
The morphology processing is herein described with respect to the high luminance-high signal level type of image signal.
(Application to Detection of Calcified Patterns)
In order for a calcified pattern to be detected, it is considered to employ a difference method, in which a smoothed image signal is subtracted from the original image signal. However, with a simple smoothing method, it is difficult to discriminate the calcified pattern from an elongated non-calcified pattern (for example, a pattern of the mammary gland, a blood vessel, mammary gland supporting tissues, or the like). Therefore, Kobatake of Tokyo University of Agriculture and Technology, et al. have proposed a morphology filter, which is represented by Formula (9) shown below and is based upon the opening operation using a multiply structure element. [Reference should be made to xe2x80x9cExtraction of Small Calcified Patterns with A Morphology Filter Using A Multiply Structure Element,xe2x80x9d Collected Papers of The Institute of Electronics and Communication Engineers of Japan, D-II, Vol. J75-D-II, No. 7, pp. 1170-1176, July 1992; and xe2x80x9cFundamentals of Morphology and Its Application to Mammogram Processing,xe2x80x9d Medical Imaging Technology, Vol. 12, No. 1, January 1994.]  "AutoLeftMatch"                                                                        P                =                                                                            f                      -                      max                                                              i                      ∈                                              (                                                  1                          ,                          ⋯                          ⁢                                                      xe2x80x83                                                    ,                          M                                                )                                                                              ⁢                                      xe2x80x83                                    ⁢                                      {                                                                  (                                                  f                          ⊖                          Bi                                                )                                            ⊕                      Bi                                        }                                                                                                                          =                                                                            f                      -                      max                                                              i                      ∈                                              (                                                  1                          ,                          ⋯                          ⁢                                                      xe2x80x83                                                    ,                          M                                                )                                                                              ⁢                                      xe2x80x83                                    ⁢                                      {                                          f                      Bi                                        }                                                                                                            (          9          )                    
In Formula (9), Bi (wherein i=1, 2, . . . , n) represents n number of linear structure elements, each of which has a size corresponding to the total size of m number of picture elements (in the example shown in FIG. 7, nine-picture element, four-direction structure elements are employed, and m=9, n=4). (The structure elements, as a whole, will hereinbelow be referred to as the m-picture element, n-direction multiply structure element.) In cases where the structure element Bi is set to be larger than the calcified pattern to be detected, a calcified pattern, which is a convex signal change portion finer than the structure element Bi (i.e., which is an image portion fluctuating in a spatially narrow region) and has luminance values larger than the luminance values of the surrounding portions, is removed in the opening processing. On the other hand, an elongated non-calcified pattern, such as a pattern of the mammary gland, is longer than the structure element Bi. Therefore, in cases where the inclination of the non-calcified pattern (i.e, the direction along which the non-calcified pattern extends) coincides with one of the directions of the four structure elements Bi, the non-calcified pattern remains unremoved after the opening processing, i.e. the operation of the second term of Formula (9), has been carried out. Therefore, when the smoothed image signal obtained from the opening processing (i.e. the signal representing the image, from which only the calcified pattern has been removed) is subtracted from the original image signal f, an image can be obtained which contains only the small calcified pattern. This is the concept behind Formula (9).
As described above, in cases where the image signal is of the high image density-high signal level type, the image density value of the calcified pattern is smaller than the image density values of the surrounding image portions, and the calcified pattern constitutes a concave signal change portion with respect to the surrounding portions. Therefore, the closing processing is applied in lieu of the opening processing, and Formula (10) shown below is applied in lieu of Formula (9).   "AutoLeftMatch"                                                                        P                =                                                                            f                      -                      min                                                              i                      ∈                                              (                                                  1                          ,                          ⋯                          ⁢                                                      xe2x80x83                                                    ,                          M                                                )                                                                              ⁢                                      xe2x80x83                                    ⁢                                      {                                                                  (                                                  f                          ⊕                          Bi                                                )                                            ⊖                      Bi                                        }                                                                                                                          =                                                                            f                      -                      min                                                              i                      ∈                                              (                                                  1                          ,                          ⋯                          ⁢                                                      xe2x80x83                                                    ,                          M                                                )                                                                              ⁢                                      xe2x80x83                                    ⁢                                      {                                          f                      Bi                                        }                                                                                                            (          10          )                    
The closing processing carried out with Formula (10), which is an example of the morphology operation, will hereinbelow be described in detail.
Specifically, the morphology operation is carried out on the image density value Sorg, which is represented by the high image density-high signal level type of image signal. With the morphology operation, the maximum value processing (i.e., the dilation processing) is carried out on the image signal, which has a distribution of the image density value Sorg indicated by, for example, the solid line in FIG. 8A, by using a linear structure element B, which is constituted of three picture elements and is shown in FIG. 8B. As a result, an image density value Si of a certain picture element of interest is converted into Sixe2x80x2, which takes the maximum value Si+1 of the values of the three adjacent picture elements (determined by the structure element B) having their center at the picture element of interest. The operation is carried out for all of the picture elements constituting the image, each of them being taken as the picture element of interest. In this manner, the image signal having the distribution of the image density value Sorg indicated by the solid line in FIG. 8A is converted into the maximum value signal having the distribution of the image density value Sorg"", which is indicated by the broken line in FIG. 8A.
Thereafter, the minimum value processing (i.e., the erosion processing) is carried out on the maximum value signal, which has been obtained from the maximum value processing, by using the structure element B. As a result, the maximum value signal Si, corresponding to the picture element of interest indicated by the broken line in FIG. 8A is converted into Sixe2x80x3 (=Si), which takes the minimum value Sixe2x88x921xe2x80x2 of the values of the three adjacent picture elements having their center at the picture element of interest. The operation is carried out for all of the picture elements constituting the image, each of them being taken as the picture element of interest. In this manner, the minimum value signal Sorgxe2x80x3 having the distribution indicated by the chained line in FIG. 8A is obtained from the minimum value processing. The image signal indicated by the chained line in FIG. 8A has the distribution such that the image portion corresponding to the signal change portion, at which the original image signal Sorg fluctuates in a spatially narrower range than the size of the structure element B, has been eliminated, and such that the image portion corresponding to the signal change portion, at which the original image signal Sorg fluctuates in a spatially wider range than the size of the structure element B, and the image portion, at which the original image signal Sorg does not fluctuates, are kept in the original forms. More specifically, the aforesaid processing (i.e., the closing processing) serves as the processing for smoothing the image density distribution from the high image density side.
The value having been obtained from the closing processing (i.e., the value having been obtained by carrying out the maximum value processing on the original image signal Sorg and then carrying out the minimum value processing) is subtracted from the original image signal Sorg, and a value Smor is thereby obtained. The thus obtained value Smor represents the image portion corresponding to the signal change portion, at which the signal value fluctuates in a spatially narrower range than the size of the structure element B and which has been eliminated by the aforesaid closing operation.
Fundamentally, an image signal represents spatial coordinates (x, y), which constitute a two-dimensional element, and a signal value f(x, y), which constitutes a third dimensional element. However, in the foregoing, as an aid in facilitating the understanding, the morphology operation is described with respect to the one-dimensional image signal distribution curve, which appears in a predetermined cross section of the image expanded in the two-dimensional plane.
Therefore, actually, it is necessary for the foregoing explanation to be applied to a two-dimensional image. Also, for the processing of a two-dimensional image, the multiply structure element is employed.
The skeleton processing in accordance with the morphology operation will be described hereinbelow.
Ordinarily, the skeleton processing is carried out for extracting skeletons of figures. A skeleton can be considered as being a set of center points of circular disks inscribed in a figure. Specifically, for example, as for the figures, which are indicated by medium-thick solid lines in FIGS. 9A through 9E, the skeletons of the figures are those indicated by the thick solid lines.
How the skeleton processing is carried out in accordance with the aforesaid morphology operation will be described hereinbelow. In such cases, the skeleton processing may be represented by Formula (11) or Formula (12) shown below.                                                         S              ⁢                              xe2x80x83                            ⁢              mor                        =                                                            ⋃                  N                                                  λ                  =                  n1                                            ⁢                              {                                  xe2x80x83                                ⁢                                                                            max                                                                        i                          =                          1                                                ,                        ⋯                        ⁢                                                  xe2x80x83                                                ,                        n                                                              ⁢                                          xe2x80x83                                        ⁢                                          (                                                                        S                          ⁢                                                      xe2x80x83                                                    ⁢                          org                                                ⊖                                                  λ                          ⁢                                                      xe2x80x83                                                    ⁢                          Bi                                                                    )                                                        -                                                              ⁢                                    max                                                i                  =                  1                                ,                ⋯                ⁢                                  xe2x80x83                                ,                n                                      ⁢                          xe2x80x83                        ⁢                                          (                                                      S                    ⁢                                          xe2x80x83                                        ⁢                    org                                    ⊖                                      λ                    ⁢                                          xe2x80x83                                        ⁢                    Bi                                                  )                            B                                      }                            (        11        )            
wherein the expression xxe2x88x92xcexY represents xcex times of Minkowski difference operations (erosion processings) carried out with the structure element Y and on the image signal X, the expression (Xxe2x88x92xcexY)y represents the opening processing carried out with the structure element Y and on the image signal (Xxe2x88x92xcexY), and U {} represents the union of sets of {} with xcex=n1, n1+1, . . . , N.                                                         S              ⁢                              xe2x80x83                            ⁢              mor                        =                                                            ⋃                  N                                                  λ                  =                  n1                                            ⁢                              xe2x80x83                            ⁢                              {                                                                            min                                                                        i                          =                          1                                                ,                        ⋯                        ⁢                                                  xe2x80x83                                                ,                        n                                                              ⁢                                          xe2x80x83                                        ⁢                                          (                                                                        S                          ⁢                                                      xe2x80x83                                                    ⁢                          org                                                ⊕                                                  λ                          ⁢                                                      xe2x80x83                                                    ⁢                          Bi                                                                    )                                                        -                                                              ⁢                                    min                                                i                  =                  1                                ,                ⋯                ⁢                                  xe2x80x83                                ,                n                                      ⁢                          xe2x80x83                        ⁢                                          (                                                      S                    ⁢                                          xe2x80x83                                        ⁢                    org                                    ⊕                                      λ                    ⁢                                          xe2x80x83                                        ⁢                    Bi                                                  )                            B                                      }                            (        12        )            
wherein the expression X⊕xcexY represents xcex times of Minkowski sum operations (dilation processings) carried out with the structure element Y and on the image signal X, the expression (X⊕xcexY)Y represents the closing processing carried out with the structure element Y and on the image signal (X⊕xcexY), and U {} represents the union of sets of {} with xcex=n1, n1+1, . . . , N.
Formula (11) or Formula (12) is selected in accordance with whether the image is represented by the high image density-high signal level type of image signal or the high luminance-high signal level type of image signal. In cases where the skeleton of an image portion having a low image density (a high luminance) is to be extracted from the image, which is represented by the high image density-high signal level type of image signal, Formula (11) is employed. In cases where the skeleton of an image portion having a low luminance (a high image density) is to be extracted from the image, which is represented by the high luminance-high signal level type of image signal, Formula (12) is employed. There is no substantial difference in effects between Formula (11) and Formula (12).
For example, as for an image formed on negative film (an image represented by the high image density-high signal level type of image signal), the image density of the bone pattern is lower than the image density of the other image portions. Also, the image density of a portion, at which a bone trabecula pattern is located, is low, and the image density of a portion, at which no bone trabecula pattern is located, is high. In such cases, the skeleton processing is carried out with respect to the bone trabecula pattern, which has a lower image density than the image density of the surrounding areas. Therefore, in such cases, Formula (11) may be employed.
FIG. 10 shows an example of the skeleton processing carried out with Formula (11) by employing a circle having a radius r as the structure element B. In FIG. 10, the skeleton processing is carried out on the figure, in which the region outward from the contour of the figure has a high image density, and the region inward from the contour of the figure has a low image density.
As illustrated along the top row in FIG. 10, the erosion processing is firstly carried out on the figure by using the structure element B. At the stage of xcex=0 (0""th erosion processing with the structure element B), no change occurs on the figure.
At the stage of xcex=1 (first erosion processing with the structure element B), the figure is eroded inwardly by a depth corresponding to the radius r of the structure element B.
At the stage of xcex=2 (second erosion processing with the structure element B), the portion projecting from the circle portion of the figure disappears perfectly.
The same operation is repeated. At the stage of xcex=Nxe2x88x921 (Nxe2x88x921""th erosion processing with the structure element B), the figure is eroded to the circle having a radius not larger than the radius r.
The second row in FIG. 10 shows the figures obtained by carrying out the opening processing with the structure element B and on the images, which have been obtained from the respective stages of the erosion processing (xcex=0, 1, 2, . . . , Nxe2x88x921, N) with the structure element B.
The third row in FIG. 10 shows the figures obtained by subtracting the figures illustrated along the second row from the figures illustrated along the top row, which figures have been obtained at the corresponding stages of the processing.
As illustrated along the third row in FIG. 10, at the stage of xcex=1, the skeleton element at the portion, which projects from the circle portion of the original figure, is extracted. Also, at the stage of xcex=Nxe2x88x921, the skeleton element of the circle portion of the original figure is extracted.
As described above, Formula (11) represents the operations for carrying out the erosion processing on the original figure, thereafter carrying out the opening processing on the resulting figures, subtracting the figures from each other, which have been obtained at the corresponding stages of the processing, and calculating the union of sets of the results of the subtraction.
Formula (12) is efficient for extracting the skeleton elements for a figure, in which the relationship of the image density levels is reverse to the relationship in Formula (11). Formula (12) represents the operations for carrying out the dilation processing on the original figure, thereafter carrying out the closing processing on the resulting figures, subtracting the figures from each other, which have been obtained at the corresponding stages of the processing, and calculating the union of sets of the results of the subtraction, the skeleton elements being thereby extracted.
As the union of sets in each of Formula (11) and Formula (12), the union of sets of only the comparatively large n1 values, e.g. only the union of sets of xcex=2, 3, 4, 5, and so on, excluding n1=0, 1, should preferably be employed, and the skeleton elements obtained in this manner should preferably be displayed. In such cases, a change in the condition of the bone trabeculae can be found more easily. Specifically, at the stages of xcex=0 and 1, noise components having a markedly high frequency are also extracted. By the exclusion of the noise components from the union of sets, an image can be obtained, which has good image quality and can serve as an effective tool in, particularly, the efficient and accurate diagnosis.
The morphology operation and the skeleton processing are carried out in the manner described above.
In lieu of the ordinary radiation image of the object, which contains the bone tissue, an energy subtraction image may be subjected to the emphasis processing in accordance with the morphology operation. The energy subtraction image is obtained by carrying out extraction or emphasis of the bone tissue pattern in accordance with two or more radiation images for energy subtraction processing, which radiation images have been formed with two or more kinds of radiation having different energy distributions.
A bone measurement apparatus in accordance with the present invention is characterized by carrying out bone tissue pattern emphasis processing in accordance with a morphology operation on an image signal, which represents a radiation image, thereby extracting or emphasizing the pattern of a structure of the bone tissue, and calculating an index value, which represents a condition of the structure of the bone tissue, in accordance with an image, which represents the extracted or emphasized pattern of the structure of the bone tissue.
Specifically, the present invention also provides a bone measurement apparatus, comprising a bone structure index value calculating means for calculating an index value representing a condition of a structure of a bone tissue,
wherein the apparatus further comprises a morphology operation means for carrying out bone tissue pattern emphasis processing on a radiation image of an object, which contains at least the bone tissue, the bone tissue pattern emphasis processing being carried out in accordance with a morphology operation, and
the bone structure index value calculating means carries out index value acquisition processing on a bone tissue image, which has been obtained from the bone tissue pattern emphasis processing and represents an emphasized pattern of the structure of the bone tissue.
In the bone measurement apparatus in accordance with the present invention, the bone tissue, the condition of the structure of the bone tissue, the index value, the bone tissue pattern emphasis processing in accordance with the morphology operation, and the skeleton processing have the same meanings as those in the aforesaid bone measurement method in accordance with the present invention.
With the bone measurement method and apparatus in accordance with the present invention, the bone tissue pattern emphasis processing in accordance with the morphology operation, such as the skeleton processing, is carried out on the image signal representing the radiation image. The pattern of the structure of the bone tissue can thus be extracted or emphasized accurately in the manner non-invasive to the object. In accordance with the image, which represents the extracted or emphasized pattern of the structure of the bone tissue, the index value representing the condition of the structure of the bone tissue, such as the index value in accordance with the star volume technique or the index value in accordance with the node-strut analysis technique, is calculated. In this manner, information representing the condition of the structure of the bone tissue, which information is useful for, particularly, osteoporosis, can be obtained as the quantitative index value.